Optimal simple rule

  1. What do you mean with
Dynare is unable to find a solution

When I run the code with the unstable version, I get

which is a solution

  1. It is not unheard of that optimal parameters may be infinity (essentially full stabilization). In those cases, people often restrict the parameter range. In the unstable version, you can use

osr_param_bounds; phiP, -1, 1; end;

  1. What do you mean with

You want a welfare function that is maximized using that parameter?